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\:0431\:043e\:043b\:044c\:0448\:0438\:0445 \[Omega]", "Section"],

Cell[BoxData[
    \(abcpic[list_] := 
      Block[{\[Omega]num, a, b, c, a0, b0, c0, minnum, tri}, 
        minnum = 
          First[Flatten[
              Position[list, _?\((Last[#] == Min[Last /@ list] &)\), {1}, 
                Heads -> False]]]; \[IndentingNewLine]Which[
          minnum \[Equal] 
            1, {a0, b0, 
              c0} = {list\[LeftDoubleBracket]1, 
                2\[RightDoubleBracket], \(list\[LeftDoubleBracket]\(-1\), 2\
\[RightDoubleBracket] - list\[LeftDoubleBracket]1, 2\[RightDoubleBracket]\)\/\
\(list\[LeftDoubleBracket]\(-1\), 1\[RightDoubleBracket] - list\
\[LeftDoubleBracket]1, 1\[RightDoubleBracket]\), 
              list\[LeftDoubleBracket]1, 
                1\[RightDoubleBracket]}, \[IndentingNewLine]minnum \[Equal] 
            Length[list], {a0, b0, 
              c0} = {list\[LeftDoubleBracket]\(-1\), 
                2\[RightDoubleBracket], \
\(-\(\(list\[LeftDoubleBracket]\(-1\), 2\[RightDoubleBracket] - 
                      list\[LeftDoubleBracket]1, 
                        2\[RightDoubleBracket]\)\/\(list\[LeftDoubleBracket]\(\
-1\), 1\[RightDoubleBracket] - 
                      list\[LeftDoubleBracket]1, 
                        1\[RightDoubleBracket]\)\)\), 
              list\[LeftDoubleBracket]\(-1\), 
                1\[RightDoubleBracket]}, \[IndentingNewLine]True, \
\[IndentingNewLine]tri = 
            Take[list, {minnum - 1, minnum + 1}]; \[IndentingNewLine]Off[
            Solve::ifun]; \[IndentingNewLine]{a0, b0, c0} = {a, b, c} /. 
              First[Solve[
                  MapThread[a + b\ Abs[#1 - c] == #2 &, Transpose[tri]], {a, 
                    b, c}]]; On[Solve::ifun]]; \[IndentingNewLine]{a, b, c} /. 
          FindFit[list, 
            a + b\ Abs[\[Omega] - c], {{a, a0}, {b, b0}, {c, 
                c0}}, \[Omega]]]\)], "Input"],

Cell[CellGroupData[{

Cell["\:041c\:0430\:043b\:044b\:0435 Re \:0438 \:0431\:043e\:043b\:044c\:0448\
\:0438\:0435 G", "Subsection"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(res = 
        ReadResult["\<kcrit11.dat\>", False];\)\), "\[IndentingNewLine]", 
    \({Relist, Glist, \[Omega]list}\)}], "Input"],

Cell[BoxData[
    \({{27, 50.653000000000006`, 85.18400000000003`, 132.65099999999998`, 
        195.112`, 274.625`, 373.2479999999999`, 493.0389999999999`, 
        636.0559999999999`, 804.3570000000002`, 1000.`, 1225.0429999999997`, 
        1481.5439999999996`, 1771.561`, 2097.1519999999996`, 2460.375`, 
        2863.2879999999996`, 3307.948999999999`, 3796.4159999999997`, 
        4330.746999999998`, 4913.`, 5545.232999999999`, 6229.503999999998`, 
        6967.870999999998`, 7762.391999999997`}, {27, 50.653000000000006`, 
        85.18400000000003`, 132.65099999999998`, 195.112`, 274.625`, 
        373.2479999999999`, 493.0389999999999`, 636.0559999999999`, 
        804.3570000000002`, 1000.`, 1225.0429999999997`, 1481.5439999999996`, 
        1771.561`, 2097.1519999999996`, 2460.375`, 2863.2879999999996`, 
        3307.948999999999`, 3796.4159999999997`, 4330.746999999998`, 4913.`, 
        5545.232999999999`, 6229.503999999998`, 6967.870999999998`, 
        7762.391999999997`}, {\(-11250\), \(-7200\), \(-4050\), \(-1800\), \
\(-450\), 0, 450, 1800, 4050, 7200, 11250}}\)], "Output"]
}, Open  ]],

Cell[BoxData[
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                res\[LeftDoubleBracket]Renum, Gnum, 
                  All\[RightDoubleBracket]], All, 
            DisplayFunction \[Rule] Identity, 
            PlotLabel -> "\<Re=\>" <> 
                ToString[
                  Relist\[LeftDoubleBracket]
                    Renum\[RightDoubleBracket]] <> "\<;G=\>" <> 
                ToString[
                  Glist\[LeftDoubleBracket]
                    Gnum\[RightDoubleBracket]]], {Renum, 1, Length[Relist], 
            3}, {Gnum, 1, Length[Glist], 3}]];\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
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          Table[FindFit[\({Last[First[#]], 1/Last[#]} &\) /@ 
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              a + b\ Abs[w - c], {a, b, c}, w], {Renum, 
              Length[Relist]}, {Gnum, Length[Glist]}];\)\)], "Input"],

Cell[BoxData[
    \(\(\[Omega]func = 
        Table[Block[{list = \({Last[First[#]], 1\/Last[#]} &\) /@ 
                  res\[LeftDoubleBracket]Renum, Gnum, 
                    All\[RightDoubleBracket], \[Omega]num, a, b, 
              c}, {c, a} = \(Select[list, 
                  Last[#] == 
                      Min[Last /@ 
                          list] &]\)\[LeftDoubleBracket]1\[RightDoubleBracket]\
; \[Omega]num = First[Flatten[Position[First /@ list, c]]]; {a, \(-b\), c} /. 
              FindFit[Take[list, \[Omega]num], b \((w - c)\) + a, {b}, 
                w]]\[IndentingNewLine], {Renum, 1, Length[Relist]}, {Gnum, 
            Length[Glist]}];\)\)], "Input"],

Cell[BoxData[
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        Table[Block[{list = 
                Take[\({Last[First[#]], 1\/Last[#]} &\) /@ 
                    res\[LeftDoubleBracket]Renum, Gnum, 
                      All\[RightDoubleBracket], 
                  Floor[Length[\[Omega]list]\/2]], \[Omega]num, a, c, 
              bs}, {c, 
                a} = \(Select[list, 
                  Last[#] == 
                      Min[Last /@ 
                          list] &]\)\[LeftDoubleBracket]1\[RightDoubleBracket]\
; \[Omega]num = 
              First[Flatten[
                  Position[First /@ list, 
                    c]]]; \[IndentingNewLine]bs = \(-b\) /. 
                FindFit[Take[list, \[Omega]num], b \((w - c)\) + a, {b}, 
                  w]; \[IndentingNewLine]{a - Abs[c] bs, bs, 
              0}]\[IndentingNewLine], {Renum, 1, Length[Relist]}, {Gnum, 
            Length[Glist]}];\)\)], "Input"]
}, Open  ]],

Cell[BoxData[
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        a + b\ Abs[\[Omega] - c] /. 
          FindFit[\({\(First[#]\)\[LeftDoubleBracket]3\[RightDoubleBracket], 
                  1\/Last[#]} &\) /@ 
              res\[LeftDoubleBracket]Renum, Gnum, All\[RightDoubleBracket], 
            a + b\ Abs[\[Omega] - c], {a, b, 
              c}, \[Omega]]; \[IndentingNewLine]g1 = 
        ListPlot[
          Evaluate[\({\(First[#]\)\[LeftDoubleBracket]3\[RightDoubleBracket], 
                  1\/Last[#]} &\) /@ 
              res\[LeftDoubleBracket]Renum, Gnum, 
                All\[RightDoubleBracket]]]; \[IndentingNewLine]g2 = 
        Plot[\[Omega]f, {\[Omega], First[\[Omega]list], 
            Last[\[Omega]list]}]; \[IndentingNewLine]f3 = \(#1 + #2\ Abs[\
\[Omega] - #3] &\)[
          Sequence @@ 
            Block[{list = \({Last[First[#]], 1\/Last[#]} &\) /@ 
                    res\[LeftDoubleBracket]Renum, Gnum, 
                      All\[RightDoubleBracket], \[Omega]num, a, b, 
                c}, {c, 
                  a} = \(Select[list, 
                    Last[#] == 
                        Min[Last /@ 
                            list] &]\)\[LeftDoubleBracket]1\
\[RightDoubleBracket]; \[Omega]num = 
                First[Flatten[Position[First /@ list, c]]]; {a, \(-b\), c} /. 
                FindFit[Take[list, \[Omega]num], b \((w - c)\) + a, {b}, 
                  w]]]; \[IndentingNewLine]g3 = 
        Plot[f3, {\[Omega], First[\[Omega]list], 
            Last[\[Omega]list]}]; \[IndentingNewLine]Show[g1, g2, 
        g3];\[IndentingNewLine]]\)], "Input"],

Cell[BoxData[{
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        PlotRange \[Rule] Automatic];\)\), "\[IndentingNewLine]", 
    \(\(ListPlot3D[\[Omega]func[\([All, All, 2]\)], 
        PlotRange \[Rule] Automatic];\)\), "\[IndentingNewLine]", 
    \(\(ListPlot3D[\[Omega]func[\([All, All, 3]\)], 
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Cell[CellGroupData[{

Cell["\:0421\:0442\:0430\:0440\:044b\:0439 \:0432\:0430\:0440\:0438\:0430\
\:043d\:0442", "Subsubsection"],

Cell[BoxData[
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              list = \({Abs[\(First[#]\)\[LeftDoubleBracket]3\
\[RightDoubleBracket]], 1\/Last[#]} &\) /@ 
                  res\[LeftDoubleBracket]Renum, Gnum, 
                    All\[RightDoubleBracket], fitsol}, 
            b = ListLimit[Take[dif[list], 10], CutValues \[Rule] False, 
                ApproximationReport \[Rule] None, 
                MaxDegree \[Rule] 7]; \[IndentingNewLine]fitsol = 
              FindFit[list, a + b\ Abs[w - c], {{a, 0}, {c, 0}}, 
                w]; \[IndentingNewLine]{a, b, c} /. 
              fitsol\[IndentingNewLine]], {Renum, Length[Relist]}, {Gnum, 
            Length[Glist]}];\)\)], "Input"],

Cell[CellGroupData[{

Cell["\:041a\:043e\:044d\:0444\:0444\:0438\:0446\:0438\:0435\:043d\:0442 a", \
"Subsubsection"],

Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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        Range[Length[Relist]]\)], "Input"],

Cell[BoxData[
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\[InvisibleSpace]\)\) + 
        0.000012043517877734347`\ G\^2, \(\(0.5727748466864662`\)\(\
\[InvisibleSpace]\)\) + 
        0.0000268005605683607`\ G\^2, \(\(0.6335415120497435`\)\(\
\[InvisibleSpace]\)\) + 
        0.00004730650582352557`\ G\^2, \(\(0.7253515633821106`\)\(\
\[InvisibleSpace]\)\) + 0.0000736718190247656`\ G\^2}\)], "Output"]
}, Open  ]],

Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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  ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {0.164509, 0.0382136, \
0.00301006, 0.000396865}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(Fit[Transpose[{Relist, #}], r\^Range[0, 2], r] &\) /@ 
      Transpose[Gfun]\)], "Input"],

Cell[BoxData[
    \({\(\(90.58109330037401`\)\(\[InvisibleSpace]\)\) - 
        179.90599227400685`\ r + 
        91.41946216019339`\ r\^2, \(\(0.006530978782212269`\)\(\
\[InvisibleSpace]\)\) + 0.1974094131053309`\ r - 
        0.09685778809727652`\ r\^2}\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(\(Plot[#, {r, 0.2, 1}] &\) /@ %;\)\)], "Input"],

Cell[BoxData[
    \(\(Show /@ Transpose[{%153, %201}];\)\)], "Input"],

Cell[BoxData[{
    \(\(ListPlot3D[\[Omega]func[\([All, All, 3]\)], 
        PlotRange \[Rule] All];\)\), "\[IndentingNewLine]", 
    \(\(ListPlot3D[
        Outer[Function[{R, 
              G}, \((90.5811 - 179.906\ R + 
                  91.4195\ R^2)\) + \((0.00653098 + 0.197409\ R - 
                    0.0968578\ R^2)\)\ G], Relist, Glist], 
        PlotRange \[Rule] All];\)\)}], "Input"]
}, Closed]],

Cell[CellGroupData[{

Cell["\:041d\:0430\:0445\:043e\:0436\:0434\:0435\:043d\:0438\:0435 \:043f\
\:0438\:043a\:043e\:0432 \:0443 \[Omega] \:0432 \
\:0441\:043f\:0438\:0441\:043a\:0435", "Text"],

Cell[BoxData[{
    \(\(\[Omega]pic[res_, Renum_, Gnum_] := 
        Block[{list = 
              res\[LeftDoubleBracket]Renum, Gnum, 
                All\[RightDoubleBracket]}, \(Select[list, 
              Last[#] == Max[Last /@ list] &]\)\[LeftDoubleBracket]1, 1, 
            3\[RightDoubleBracket]];\)\), "\[IndentingNewLine]", 
    \(\(\[Omega]pic[Renum_, Gnum_] := 
        Block[{list = 
              res5\[LeftDoubleBracket]Renum, Gnum, 
                All\[RightDoubleBracket]}, \(Select[list, 
              Last[#] == Max[Last /@ list] &]\)\[LeftDoubleBracket]1, 1, 
            3\[RightDoubleBracket]];\)\)}], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Outer[\[Omega]pic, Range[Length[Relist]], Range[Length[Glist]]] // 
      TableForm\)], "Input"],

Cell[BoxData[
    TagBox[GridBox[{
          {"20", "20", "20", \(-45\), \(-45\), \(-180\)},
          {\(-20\), \(-20\), \(-20\), \(-20\), \(-45\), \(-180\)},
          {"5", "5", "5", \(-20\), \(-45\), \(-180\)},
          {"5", "5", "5", \(-20\), \(-45\), \(-180\)},
          {"5", "5", "5", \(-5\), \(-45\), \(-180\)}
          },
        RowSpacings->1,
        ColumnSpacings->3,
        RowAlignments->Baseline,
        ColumnAlignments->{Left}],
      Function[ BoxForm`e$, 
        TableForm[ BoxForm`e$]]]], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(With[{res = \(Drop[#, 1] &\) /@ ReadResult["\<kcrit1.dat\>", False]}, 
          Outer[\[Omega]pic[res, #1, #2] &, Range[Length[Relist]], 
            Range[Length[Glist] - 1]]] // ListDensityPlot;\)\)], "Input"]
}, Closed]],

Cell[BoxData[
    \(asimptot[R_, 
        G_, \[Omega]_] := \((\((\(-0.2463\) + 1.9826195\ R - 
                1.03322\ R\^2)\) + 
            0.0000735373\ \(R\^2\) G\^2)\) + \((0.00419464 + 0.0751365\ R - 
              0.0446854\ R\^2 + 
              0.000984302\ R\^2\ G)\)\ Abs[\[Omega] - \((90.5811 - 
                  179.906\ R + 
                  91.4195\ R\^2)\) - \((0.00653098 + 0.197409\ R - 
                    0.0968578\ R\^2)\)\ G]\)], "Input"]
}, Closed]],

Cell[CellGroupData[{

Cell["\:041e\:0441\:043d\:043e\:0432\:043d\:043e\:0439 \:0432\:0430\:0440\
\:0438\:0430\:043d\:0442", "Subsubsection"],

Cell[CellGroupData[{

Cell["\:041a\:043e\:044d\:0444\:0444\:0438\:0446\:0438\:0435\:043d\:0442 a", \
"Subsubsection"],

Cell[BoxData[
    \(\(g1 = \(PrintRange[
              Transpose[{Glist, \[Omega]func\[LeftDoubleBracket]#, All, 
                    1\[RightDoubleBracket]}]] &\) /@ 
          Range[Length[Relist]];\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Gfun = \(Fit[
            Drop[Transpose[{Glist, \[Omega]func\[LeftDoubleBracket]#, All, 
                    1\[RightDoubleBracket]}], 3], {1, G}, G] &\) /@ 
        Range[Length[Relist]]\)], "Input"],

Cell[BoxData[
    \({\(\(0.014874759966896337`\)\(\[InvisibleSpace]\)\) + 
        0.00015920726892424244`\ G, \(\(0.09197856117597852`\)\(\
\[InvisibleSpace]\)\) + 
        0.00004168192712437323`\ G, \(\(0.07019647011237372`\)\(\
\[InvisibleSpace]\)\) - 
        4.308672342355257`*^-6\ G, \(\(0.09165969658557699`\)\(\
\[InvisibleSpace]\)\) - 
        0.0000885197253495976`\ G, \(\(0.1142181250835905`\)\(\
\[InvisibleSpace]\)\) - 0.00019575912471582902`\ G}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \({d, e} = \(Transpose[{Relist, #}] &\) /@ 
        Transpose[\(CoefficientList[#, G] &\) /@ Gfun]\)], "Input"],

Cell[BoxData[
    \({{{0.2`, 0.014874759966896337`}, {0.4`, 
          0.09197856117597852`}, {0.6000000000000001`, 
          0.07019647011237372`}, {0.8`, 0.09165969658557699`}, {1.`, 
          0.1142181250835905`}}, {{0.2`, 0.00015920726892424244`}, {0.4`, 
          0.00004168192712437323`}, {0.6000000000000001`, \
\(-4.308672342355257`*^-6\)}, {0.8`, \(-0.0000885197253495976`\)}, {1.`, \
\(-0.00019575912471582902`\)}}}\)], "Output"]
}, Open  ]],

Cell[BoxData[{
    \(\(PrintRange[d];\)\), "\[IndentingNewLine]", 
    \(\(PrintRange[e];\)\)}], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Fit[d, {1, r, r\^2, r\^3}, r]\)], "Input"],

Cell[BoxData[
    \(\(-0.1558210830671727`\) + 1.223428705548775`\ r - 
      1.9922266393018688`\ r\^2 + 1.041469732265593`\ r\^3\)], "Output",
  GeneratedCell->False,
  CellAutoOverwrite->False]
}, Open  ]],

Cell[BoxData[
    \(\(Show[%111, Plot[%118, {r, 0, 1}]];\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Fit[e, {1, r}, r]\)], "Input"],

Cell[BoxData[
    \(\(\(0.00023450066665440074`\)\(\[InvisibleSpace]\)\) - 
      0.0004200672198770566`\ r\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(Show[%112, Plot[%, {r, 0, 1}]];\)\)], "Input"],

Cell[BoxData[{
    \(\(ListPlot3D[\[Omega]func[\([All, All, 1]\)], 
        PlotRange \[Rule] {\(-0.1\), 0.1}];\)\), "\[IndentingNewLine]", 
    \(\(ListPlot3D[
        Outer[Function[{Re, G}, 
            Evaluate[\((\(-0.155821\) + 1.22343\ Re - 1.99223\ Re^2 + 
                    1.04147\ Re^3)\) + \((0.000234501 - 0.000420067\ Re)\) 
                  G]], Relist, Glist]];\)\)}], "Input"]
}, Closed]],

Cell[CellGroupData[{

Cell["\:041a\:043e\:044d\:0444\:0444\:0438\:0446\:0438\:0435\:043d\:0442 b", \
"Subsubsection"],

Cell[BoxData[
    \(\(blist = \(Transpose[{Glist, \[Omega]func\[LeftDoubleBracket]#, All, 
                  2\[RightDoubleBracket]}] &\) /@ 
          Range[Length[Relist]];\)\)], "Input"],

Cell[BoxData[
    \(\(g1 = PrintRange /@ \(dif /@ blist\);\)\)], "Input"],

Cell[BoxData[
    \(f = \(ListLimit[# // dif, ApproximationReport \[Rule] None] &\) /@ 
        blist\)], "Input"],

Cell[BoxData[
    RowBox[{\(FindRoot::"cvmit"\), \(\(:\)\(\ \)\), "\<\"Failed to converge \
to the requested accuracy or precision within \\!\\(100\\) iterations. \\!\\(\
\\*ButtonBox[\\\"More\[Ellipsis]\\\", ButtonStyle->\\\"RefGuideLinkText\\\", \
ButtonFrame->None, ButtonData:>\\\"FindRoot::cvmit\\\"]\\)\"\>"}]], "Message"],

Cell[BoxData[
    \({0.000027471756965688477`, 0.00010347444672100842`, 
      0.00027197586492317847`, 0.0005457009657700473`, 
      0.0008797951553475507`}\)], "Output"],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(PrintRange[Transpose[{Relist, f}]];\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Fit[Transpose[{Relist, f}], {1, r, r\^2}, r]\)], "Input"],

Cell[BoxData[
    \(\(\(0.000032324984346198916`\)\(\[InvisibleSpace]\)\) - 
      0.0002581490898559035`\ r + 0.0011096547898019043`\ r\^2\)], "Output"]
}, Open  ]]
}, Open  ]],

Cell[BoxData[
    \(\(Show[Plot[%, {r, 0, 1}], %135];\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(slist = 
      Transpose[{Relist, 
          s /. MapThread[
              FindFit[#1, s + #2\ G, {s}, G] &, {blist, f}]}]\)], "Input"],

Cell[BoxData[
    \({{0.2`, 0.016228056536728878`}, {0.4`, 
        0.03523475252788927`}, {0.6000000000000001`, 
        0.046626738866845215`}, {0.8`, 0.04944636559830186`}, {1.`, 
        0.0500198338075908`}}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Fit[slist, {1, r, r\^2}, r]\)], "Input"],

Cell[BoxData[
    \(\(-0.0077468084017908055`\) + 0.13826647345873005`\ r - 
      0.08114074137721819`\ r\^2\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(Show[PrintRange[slist], Plot[%, {r, 0, 1}]];\)\)], "Input"],

Cell[BoxData[{
    \(\(ListPlot3D[\[Omega]func[\([All, All, 2]\)], 
        PlotRange \[Rule] {0, 0.1}];\)\), "\[IndentingNewLine]", 
    \(\(ListPlot3D[
        Outer[Function[{Re, 
              G}, \((\(-0.00774681\) + 0.138266\ Re - 
                  0.0811407\ Re^2)\) + \((0.000032325 - 0.000258149\ Re + 
                    0.00110965\ Re^2)\)\ G], Relist, Glist], 
        PlotRange \[Rule] {0, 0.1}];\)\)}], "Input"]
}, Closed]],

Cell[CellGroupData[{

Cell["\:041a\:043e\:044d\:0444\:0444\:0438\:0446\:0438\:0435\:043d\:0442 c", \
"Subsubsection"],

Cell[BoxData[
    \(\(g1 = \(PrintRange[
              Transpose[{Glist, \[Omega]func\[LeftDoubleBracket]#, All, 
                    3\[RightDoubleBracket]}], All] &\) /@ 
          Range[Length[Relist]];\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Gfun = 
      CoefficientList[\(Fit[
              Transpose[{Glist, \[Omega]func\[LeftDoubleBracket]#, All, 
                    3\[RightDoubleBracket]}], {1, G}, G] &\) /@ 
          Range[Length[Relist]], G]\)], "Input"],

Cell[BoxData[
    \({{\(-3.6523517113583974`\), \(-0.17117431914035458`\)}, \
{\(-9.90644570157607`\), \(-0.161383195461265`\)}, {\(-11.57103057125524`\), \
\(-0.1588699795049029`\)}, {\(-20.01412176181085`\), \
\(-0.14848284430314174`\)}, {\(-15.140042453615555`\), \(-0.1543749592944145`\
\)}}\)], "Output"]
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Fit[Transpose[{Glist, Gcoef[\([2]\)]}], G\^Range[0, 2], G]\)], "Input"],

Cell[BoxData[
    \(\(-0.000010869630097154471`\) - 6.897558661578069`*^-12\ G + 
      0.0007618063364352585`\ G\^2\)], "Output"]
}, Open  ]],

Cell[BoxData[{
    \(\(ListPlot3D[\[Omega]func[\([All, All, 2]\)] // Log, 
        PlotRange \[Rule] Automatic];\)\), "\[IndentingNewLine]", 
    \(\(ListPlot3D[
        Outer[Function[{Re, G}, 
            Log[\((0.0536849 + 
                    0.0139976  Re^2)\) + \((\(-0.0000108696\) + 
                      0.000761806  Re^2)\) G]], Relist, Glist], 
        PlotRange \[Rule] Automatic];\)\)}], "Input"]
}, Closed]],

Cell[CellGroupData[{

Cell["\:041a\:043e\:044d\:0444\:0444\:0438\:0446\:0438\:0435\:043d\:0442 c", \
"Subsubsection"],

Cell[BoxData[
    \(\(g1 = \(PrintRange[
              Transpose[{Glist, \[Omega]func\[LeftDoubleBracket]#, All, 
                    3\[RightDoubleBracket]}], All] &\) /@ 
          Range[Length[Relist]];\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Gfun = 
      CoefficientList[\(Fit[
              Transpose[{Glist, \[Omega]func\[LeftDoubleBracket]#, All, 
                    3\[RightDoubleBracket]}], {1, G}, G] &\) /@ 
          Range[Length[Relist]], G]\)], "Input"],

Cell[BoxData[
    \({{\(-3.6523517113583974`\), \(-0.17117431914035458`\)}, \
{\(-9.90644570157607`\), \(-0.161383195461265`\)}, {\(-11.57103057125524`\), \
\(-0.1588699795049029`\)}, {\(-20.01412176181085`\), \
\(-0.14848284430314174`\)}, {\(-15.140042453615555`\), \(-0.1543749592944145`\
\)}}\)], "Output"]
}, Open  ]],

Cell[BoxData[{
    \(\(ListPlot3D[\[Omega]func[\([All, All, 3]\)], 
        PlotRange \[Rule] All];\)\), "\[IndentingNewLine]", 
    \(\(ListPlot3D[
        Outer[Function[{Re, 
              G}, \((5.60704 - 49.7083\ Re + 
                  27.639\ Re^2)\) + \((\(-0.184553\) + 0.0735907\ Re - 
                    0.041951\ Re^2)\)\ G], Relist, Glist], 
        PlotRange \[Rule] All];\)\)}], "Input"]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\:041d\:0430\:0445\:043e\:0436\:0434\:0435\:043d\:0438\:0435 \:043f\
\:0438\:043a\:043e\:0432 \:0443 \[Omega] \:0432 \
\:0441\:043f\:0438\:0441\:043a\:0435", "Text"],

Cell[BoxData[{
    \(\(\[Omega]pic[res_, Renum_, Gnum_] := 
        Block[{list = 
              res\[LeftDoubleBracket]Renum, Gnum, 
                All\[RightDoubleBracket]}, \(Select[list, 
              Last[#] == Max[Last /@ list] &]\)\[LeftDoubleBracket]1, 1, 
            3\[RightDoubleBracket]];\)\), "\[IndentingNewLine]", 
    \(\(\[Omega]pic[Renum_, Gnum_] := 
        Block[{list = 
              res5\[LeftDoubleBracket]Renum, Gnum, 
                All\[RightDoubleBracket]}, \(Select[list, 
              Last[#] == Max[Last /@ list] &]\)\[LeftDoubleBracket]1, 1, 
            3\[RightDoubleBracket]];\)\)}], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Outer[\[Omega]pic, Range[Length[Relist]], Range[Length[Glist]]] // 
      TableForm\)], "Input"],

Cell[BoxData[
    TagBox[GridBox[{
          {"20", "20", "20", \(-45\), \(-45\), \(-180\)},
          {\(-20\), \(-20\), \(-20\), \(-20\), \(-45\), \(-180\)},
          {"5", "5", "5", \(-20\), \(-45\), \(-180\)},
          {"5", "5", "5", \(-20\), \(-45\), \(-180\)},
          {"5", "5", "5", \(-5\), \(-45\), \(-180\)}
          },
        RowSpacings->1,
        ColumnSpacings->3,
        RowAlignments->Baseline,
        ColumnAlignments->{Left}],
      Function[ BoxForm`e$, 
        TableForm[ BoxForm`e$]]]], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(With[{res = \(Drop[#, 1] &\) /@ ReadResult["\<kcrit1.dat\>", False]}, 
          Outer[\[Omega]pic[res, #1, #2] &, Range[Length[Relist]], 
            Range[Length[Glist] - 1]]] // ListDensityPlot;\)\)], "Input"]
}, Closed]],

Cell[BoxData[
    \(asimptot[R_, 
        G_, \[Omega]_] := \((\((\(-0.155821\) + 1.22343\ R - 1.99223\ R\^2 + 
                1.04147\ R\^3)\) + \((0.000234501 - 0.000420067\ R)\) 
              G)\) + \((\((\(-0.00774681\) + 0.138266\ R - 
                  0.0811407\ R\^2)\) + \((0.000032325 - 0.000258149\ R + 
                    0.00110965\ R\^2)\)\ G)\)\ Abs[
            w - \((5.60704 - 49.7083\ R + 
                  27.639\ R\^2)\) - \((\(-0.184553\) + 0.0735907\ R - 
                    0.041951\ R\^2)\)\ G]\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(asimptot[0.2, 1024, w]\)], "Input"],

Cell[BoxData[
    \(\(\(0.1716068624`\)\(\[InvisibleSpace]\)\) + 
      0.04234391080000001`\ Abs[\(\(178.8582696`\)\(\[InvisibleSpace]\)\) + 
            w]\)], "Output"],

Cell[BoxData[
    \(With[{gnum = Random[Integer, {1, Length[Glist]}], 
        Renum = Random[
            Integer, {1, 
              Length[Relist]}]}, \[IndentingNewLine]Print["\<G=\>", 
        Glist\[LeftDoubleBracket]gnum\[RightDoubleBracket], "\<;Re=\>", 
        Relist\[LeftDoubleBracket]
          Renum\[RightDoubleBracket]]; \[IndentingNewLine]g1 = 
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                1\/Last[#]} &\) /@ 
            res\[LeftDoubleBracket]Renum, gnum, 
              All\[RightDoubleBracket]]; \[IndentingNewLine]g2 = 
        Plot[asimptot[Relist\[LeftDoubleBracket]Renum\[RightDoubleBracket], 
            Glist\[LeftDoubleBracket]gnum\[RightDoubleBracket], 
            w], {w, \(-1000\), 1000}];\[IndentingNewLine]]\)], "Input"],

Cell[BoxData[
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\[InvisibleSpace]1.`\),
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  CellAutoOverwrite->False],

Cell[BoxData[
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}, Open  ]]
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Cell[CellGroupData[{

Cell["\:041c\:0430\:043b\:044b\:0435 Re \:0438 G", "Subsection"],

Cell[CellGroupData[{

Cell[BoxData[{
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Cell[BoxData[
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\(-45\), \(-20\), \(-5\), 0, 5, 20, 45, 80, 125, 180, 245, 320, 405, 500, 
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}, Open  ]],

Cell[BoxData[
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                    Gnum\[RightDoubleBracket]]], {Renum, 1, 
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Cell[BoxData[
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Cell[BoxData[{
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    \(\(\[Omega]pic[Renum_, Gnum_] := 
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                All\[RightDoubleBracket]}, \(Select[list, 
              Last[#] == 
                  Max[Last /@ 
                      list] &]\)\[LeftDoubleBracket]1\[RightDoubleBracket]];\)\
\)}], "Input"],

Cell[BoxData[
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                  Last[#] == 
                      Min[Last /@ 
                          list] &]\)\[LeftDoubleBracket]1\[RightDoubleBracket]\
; \[Omega]num = First[Flatten[Position[First /@ list, c]]]; {a, \(-b\), c} /. 
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Cell[BoxData[
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                    res\[LeftDoubleBracket]Renum, Gnum, 
                      All\[RightDoubleBracket], 
                  Floor[Length[\[Omega]list]\/2]], \[Omega]num, a, c, 
              bs}, {c, 
                a} = \(Select[list, 
                  Last[#] == 
                      Min[Last /@ 
                          list] &]\)\[LeftDoubleBracket]1\[RightDoubleBracket]\
; \[Omega]num = 
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                  Position[First /@ list, 
                    c]]]; \[IndentingNewLine]bs = \(-b\) /. 
                FindFit[Take[list, \[Omega]num], b \((w - c)\) + a, {b}, 
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Cell[CellGroupData[{

Cell[BoxData[
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\(\[Omega]num = First[Flatten[Position[First /@ list, c]]]; {a, \(-b\), c} /. 
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Cell[BoxData[
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}, Open  ]],

Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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\[Omega]] &\)[
          Sequence @@ 
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Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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      0.0017180555612477312`\ r + 0.0008045508865657042`\ r\^2\)], "Output"]
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}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]],

Cell[BoxData[
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Cell[BoxData[{
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                    3.2900887002844834*10^\((\(-6\))\) 
                      Re^2)\) + \((0.853512 + 0.00171806\ Re + 
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}, Closed]],

Cell[CellGroupData[{

Cell["\:041d\:0430\:0445\:043e\:0436\:0434\:0435\:043d\:0438\:0435 \:043f\
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Cell[BoxData[{
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    \(\(\[Omega]pic[Renum_, Gnum_] := 
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              Last[#] == Max[Last /@ list] &]\)\[LeftDoubleBracket]1, 1, 
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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        RowSpacings->1,
        ColumnSpacings->3,
        RowAlignments->Baseline,
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Cell[BoxData[
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Cell[BoxData[
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                  0.000139278\ R\^2)\) 
              G\^2)\) + \((\((7.08299 + 0.0101589\ R + 
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Cell[CellGroupData[{

Cell[BoxData[
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              All\[RightDoubleBracket]]; \[IndentingNewLine]g2 = 
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Cell[BoxData[
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}, Open  ]],

Cell["\:0411\:043e\:043b\:044c\:0448\:0438\:0435 Re \:0438 G", "Subsection"]
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Cell[CellGroupData[{

Cell["\:0411\:043e\:043b\:044c\:0448\:0438\:0435 G \:0438 Re", "Subsection"],

Cell[CellGroupData[{

Cell[BoxData[{
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Cell[BoxData[
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Cell[BoxData[
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\[RightDoubleBracket]]], {Renum, 1, Length[Relist], 2}, {\[Omega]num, 1, 
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Cell[BoxData[
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            DisplayFunction \[Rule] Identity, 
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Cell[BoxData[
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            DisplayFunction \[Rule] Identity, 
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Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[{
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Cell["\:041a\:043e\:044d\:0444\:0444\:0438\:0446\:0438\:0435\:043d\:0442 a", \
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Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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Cell[CellGroupData[{

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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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      0.0005010603768947754`\ G\)], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(Show[Plot[%, {G, 0, Last[Glist]}], %50];\)\)], "Input"],

Cell[BoxData[{
    \(\(ListPlot3D[\[Omega]func[\([All, All, 2]\)] // 
          Log];\)\), "\[IndentingNewLine]", 
    \(\(ListPlot3D[
        Outer[Function[{Re, G}, Log[\((0.215405 + 0.00050106\ G)\) Re^2]], 
          Relist, Glist]];\)\)}], "Input"]
}, Closed]],

Cell[CellGroupData[{

Cell["\:041a\:043e\:044d\:0444\:0444\:0438\:0446\:0438\:0435\:043d\:0442 c", \
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Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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      CoefficientList[\(Fit[
              Transpose[{Glist, \[Omega]func\[LeftDoubleBracket]#, All, 
                      3\[RightDoubleBracket]}] // Most, {1, G}, G] &\) /@ 
          Range[Length[Relist]], G]\)], "Input"],

Cell[BoxData[
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{1.2743616591563098`, \(-0.16594765069131517`\)}, {1.2743616591563098`, \
\(-0.16594765069131517`\)}, {1.2743616591563098`, \(-0.16594765069131517`\)}, \
{1.2743616591563098`, \(-0.16594765069131517`\)}, {1.2743616591563098`, \
\(-0.16594765069131517`\)}, {1.2743616591563098`, \(-0.16594765069131517`\)}, \
{1.2743616591563098`, \(-0.16594765069131517`\)}, {1.2743616591563098`, \
\(-0.16594765069131517`\)}, {1.2743616591563098`, \(-0.16594765069131517`\)}, \
{1.2743616591563098`, \(-0.16594765069131517`\)}, {1.2743616591563098`, \
\(-0.16594765069131517`\)}, {1.2743616591563098`, \(-0.16594765069131517`\)}, \
{1.2743616591563098`, \(-0.16594765069131517`\)}, {1.2743616591563098`, \
\(-0.16594765069131517`\)}, {1.2743616591563098`, \(-0.16594765069131517`\)}}\
\)], "Output",
  GeneratedCell->False,
  CellAutoOverwrite->False]
}, Open  ]],

Cell[BoxData[
    \(\(Show[Plot[Gfun[\([1]\)] . {1, G}, {G, 0, Last[Glist]}], 
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Cell[BoxData[{
    \(\(ListPlot3D[\[Omega]func[\([All, All, 3]\)], 
        PlotRange \[Rule] All];\)\), "\[IndentingNewLine]", 
    \(\(ListPlot3D[
        Outer[Function[{Re, G}, 1.27436 - 0.165948\ G], Relist, Glist], 
        PlotRange \[Rule] All];\)\)}], "Input"]
}, Closed]],

Cell[BoxData[
    \(asimptot[R_, 
        G_, \[Omega]_] := \((\(-1.63013\) - 
            44.7475\ R\^2)\) + \((0.00086268 + 
              0.0628674\ R\^2)\)\ G + \((0.215405 + 0.00050106\ G)\) 
          R\^2\ Abs[w - 1.27436 + 0.165948\ G]\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(asimptot[4913, 5832, w]\)], "Input"],

Cell[BoxData[
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      7.573372077499747`*^7\ \
Abs[\(\(966.5343760000001`\)\(\[InvisibleSpace]\)\) + w]\)], "Output"],

Cell[BoxData[
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        Renum = Random[
            Integer, {1, 
              Length[Relist]}]}, \[IndentingNewLine]Print["\<G=\>", 
        Glist\[LeftDoubleBracket]gnum\[RightDoubleBracket], "\<;Re=\>", 
        Relist\[LeftDoubleBracket]
          Renum\[RightDoubleBracket]]; \[IndentingNewLine]g1 = 
        PrintRange[\({\(First[#]\)\[LeftDoubleBracket]3\[RightDoubleBracket], 
                1\/Last[#]} &\) /@ 
            res\[LeftDoubleBracket]Renum, gnum, 
              All\[RightDoubleBracket]]; \[IndentingNewLine]g2 = 
        Plot[asimptot[Relist\[LeftDoubleBracket]Renum\[RightDoubleBracket], 
            Glist\[LeftDoubleBracket]gnum\[RightDoubleBracket], 
            w], {w, \(-1000\), 1000}]; \[IndentingNewLine]Show[g1, 
        g2];\[IndentingNewLine]]\)], "Input"]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell["\:0414\:0440\:0443\:0433\:0438\:0435 \:043f\:0430\:0440\:0430\:043c\
\:0435\:0442\:0440\:044b", "Section"],

Cell[BoxData[
    \(ExcludeRe[list_] := 
      Switch[ArrayDepth[list], 
        2, \({{#\[LeftDoubleBracket]1, 
                    1\[RightDoubleBracket] #\[LeftDoubleBracket]1, 
                    2\[RightDoubleBracket], #\[LeftDoubleBracket]1, 
                    1\[RightDoubleBracket] #\[LeftDoubleBracket]1, 
                    3\[RightDoubleBracket]}, 
              1\/#\[LeftDoubleBracket]2\[RightDoubleBracket]} &\) /@ list, 4, 
        ExcludeRe[Flatten[list, 2]], _, $Failed]\)], "Input"],

Cell[CellGroupData[{

Cell["\:0411\:043e\:043b\:044c\:0448\:0438\:0435 w,G,Re", "Subsection"],

Cell[BoxData[{
    \(\(res = 
        ReadResult["\<kcrit7.dat\>", True];\)\), "\[IndentingNewLine]", 
    \({Relist, Glist, \[Omega]list}\)}], "Input"],

Cell[BoxData[
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        2197, 2744, 3375, 4096, 4913, 5832, 6859, 
        8000}, {\(-1125\), \(-980\), \(-845\), \(-720\), \(-605\), \(-500\), \
\(-405\), \(-320\), \(-245\), \(-180\), \(-125\), \(-80\), \(-45\), \(-20\), \
\(-5\), 0, 5, 20, 45, 80, 125, 180, 245, 320, 405, 500, 605, 720, 845, 980, 
        1125}}\)], "Output",
  GeneratedCell->False,
  CellAutoOverwrite->False],

Cell[BoxData[
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Cell["\<\
\:041d\:0435\:0443\:0434\:0430\:0447\:043d\:0430\:044f \:043f\:043e\:043f\
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\:0438\:0442\:044c \:043d\:0430 \:043e\:0434\:043d\:043e\:0439 \:043f\:043b\
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Cell[BoxData[
    \({mink, maxk} = \({Min[#], Max[#]} &\)[Last /@ anal]\)], "Input"],

Cell[BoxData[
    \({7.686048905813082`, 27.66830545002916`}\)], "Output",
  GeneratedCell->False,
  CellAutoOverwrite->False],

Cell[BoxData[
    \(\(Show[
        Graphics[\({Hue[\(Last[#] - mink\)\/\(maxk - mink\)], 
                Disk[First[#], 2]} &\) /@ anal], 
        PlotRange \[Rule] All];\)\)], "Input"],

Cell[BoxData[
    \(\({grelist, wrelist} = Union /@ Transpose[First /@ anal];\)\)], "Input"],

Cell[BoxData[
    \(gresel[list_, gren_] := 
      Union[\({#\[LeftDoubleBracket]1, 
                2\[RightDoubleBracket], #\[LeftDoubleBracket]2\
\[RightDoubleBracket]} &\) /@ 
          Select[list, \((#\[LeftDoubleBracket]1, 
                    1\[RightDoubleBracket] \[Equal] 
                  grelist\[LeftDoubleBracket]
                    gren\[RightDoubleBracket] &)\)]]\)], "Input"],

Cell[BoxData[
    \(\(\(PrintRange[gresel[anal, #]] &\) /@ 
        Range[Length[grelist]];\)\)], "Input"],

Cell[BoxData[{
    \(\(kf = abcpic[gresel[anal, 90]];\)\), "\[IndentingNewLine]", 
    \(\(Show[
        Plot[kf\[LeftDoubleBracket]1\[RightDoubleBracket] + 
            kf\[LeftDoubleBracket]2\[RightDoubleBracket]\ Abs[\[Omega] - 
                  kf\[LeftDoubleBracket]3\[RightDoubleBracket]], {\[Omega], \
\(gresel[anal, 90]\)[\([1, 1]\)], \(gresel[anal, 90]\)[\([\(-1\), 1]\)]}], 
        PrintRange[gresel[anal, 90]]];\)\)}], "Input"],

Cell[BoxData[
    \(\(wfunc = 
        Transpose[\(abcpic[gresel[anal, #]] &\) /@ 
            Range[Length[grelist]]];\)\)], "Input"],

Cell[BoxData[
    \(\(PrintRange[
        Take[Transpose[{grelist, \@Abs[wfunc\[LeftDoubleBracket]1\
\[RightDoubleBracket]]}], 70]];\)\)], "Input"],

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